Gueye is Koeman's second signing since he took over from the sacked Roberto Martinez in mid-June, having brought in Maarten Stekelenburg from Fulham.

"Idrissa will provide quality in our squad in the midfield and we want to increase the quality in the team," said Koeman.

"He was one of the players last season with the best record in interceptions and pressing in the midfield. We need this kind of quality and I'm happy to have him joining our club."

Gueye was second only to Leicester's Premier League-winning midfielder N'Golo Kante in terms of the number of combined interceptions and tackles made across Europe's top five leagues.

He moved to Villa from Lille last summer and made 38 appearances in all competitions as Villa were relegated from the Premier League.

"I am very happy to be here at Everton and I am very happy and excited to put on the Blue shirt to start the new season here," he said.

"Everton is a big team with big players and great fans. The manager told me he is very happy to have me here and that we will have time to talk about football after.

"I am a defensive midfield player and I like making passes and also getting forward.

"I have played a season with Aston Villa which was a hard season but I think my style is good for the Premier League.

"You have to fight every game. All the teams are strong and you have to concentrate all through the game.

"Goodison Park is a very good stadium and the fans are very good too. They push their team forward and I am excited to play there."

Koeman could well be thwarted in a move for Swansea captain Ashley Williams, though.

Williams was understood to be on the verge of making a £10million move from Swansea, but on Tuesday night a City spokesman said: " We are not looking to sell him, and therefore we have turned down the offer currently on the table."

However, Manchester City's pursuit of John Stones and Chelsea's reported attempts to re-sign striker Romelu Lukaku may mean there are still a few changes to come before their campaign kicks off at home to Tottenham on August 13.